ernnot

15358~,!
NetworkWorkingGroupRequestForComments#493IJICIi15358References:282,285L·vL::.
UUpdates:NoneObsoletes:292MAY1'(i973KarlDaveAprl126,1973JimMichener,MACIraCotton,MITREKe11ey,UofI11Lidd1e,O\'Jen5I11EdMeyer,MAC.
.
GRAPHICSPROTOCOLIntroductionThisdocumentreflectsopinionsexpressedanddecisionsreachedatthesecondmeetingoftheNetworkGraphicsGroup,heldattheStanfordArtificialIntelligenceLaboratoryinlateNovember1971.
ItdescribesnartofaproposedNetworkStandardGraphicsProtocolfortransmittin~graphicsdatawithintheARPAnetwork.
Theparticularaspectsoftheprotocolcoveredinthisdocumentrelatetotheformandcontentof~raphicsinformationsentfromasourceofgraphicallnforrnatlon(anapplicationprogram,say,inthe"Servlng1I0st")toadisplaypackageforoutputtoagraphicsconsole(atthe"UsingHostll).
Thiswilltaketheformofasequenceofa-bitbytes,andwillbecalledthegraphicsoutputbytestream.
Thisdocumentisintendedtoserveasabasisfordiscussionandforexperimentationoverthenetwork.
Thisdocumentdoesnotincludeformorcontentofgraphicsinput(datasentfrOMtheUsing1I0sttotheServingHost)nordoesitcoverhO\'Itheconnectionisestab1ishedbetweenthehosts.
Aproposalfortheformerwillbegeneratedeventuallybythiscommittee;thelatteristhejoboftheConnectionCommittee(oftheNetworkGraphicsGroup).
ThisRFCdescribesthecornnandswhlchareavailableintheprotocolintermsoftheeffecttheywouldhaveattherecelvlnrr(UsingHost)end.
Clearly,sonesubroutinepackap:eisdesirableattheServingHostforusebyapplicationsintransmittinp,graphicsdata,butonthistopicthisRFCdoesnotintendtocomrnent,Itmaybeobservedbythereaderthatnofacilityisspecifiedinthisportocol,allowlngtheUsingHosttoreportlogicalerrorsinthegraphicsoutputbytestreamtot~1eServingtlost.
Suchafacilitywouldhavetobeintegratedwiththe~raphicsinputbytestream,sinceitinvolvesmostoftheproblemsrelatedtosynchronyofindependenthosts.
BackgroundThereadershouldprobablyperuseRFC282:"Graphicst'1eetingReport"byliikePadllpskvtoobtainSOMeofthefrarneworksurroundingthisdiscussionofnetwork~raphics.
AlsoitmightbevaluabletomakenoteofthemodeldescribedinRFC285:-1,'t,//"NetworkGraphics"byDonaldHuff.
L~velsandGroundRulesPertainingTheretoFunctionswithinthe~raphicsprotocolwillbeclassifiedintoanumberoflevelsdependingpartlyonhowdifficultitistoimplementthosefunctions.
ItisintendedthatanyhostwhichclaimstoimplementthefunctionsoflevelNmustimplementalllowerlevelsaswell.
Thus,itisenvisionedthatsiteswillimplementlevelsincremently.
·Implementationswillbeimprovedasacontinuingprocesstoincludemoreandmorefunctions,anditisintendedthateachimplementationwillbeabletoidentifyitsownleveltoagraphicsprotocolataremotesitewhichisrequestingagraphicsinterchange.
Asideresultisthateachsitewillbeabletodetermineitsownprioritiesincommittingprogrammerstothegraphicsprotocolasopposedtootherefforts.
ItisalsoourintentionthztlrnolementetlonoflevelNwillrequirenoknowledgeoflevelN+l.
Thusasitecanimplementalevelinthe(reasonably)firmknowledgethatnochangesathigher+eve-lw·i-llalterthelevelimplemented.
AtsometimeitmaybedecidedbytheNetworkGraphicsGrouptoredefinealevelwhichhaspreviouslybeenfirnedup.
ItisnotourintentionthatthisshallhappenbutonemustrecognizethattheproposedGraphicsProtocolisexperimentalannmayhavetobechanged.
Onefurthergroundrule:astreamofcommandsanddatawhichisvalidatagivenlevel,K,shallproduce"identical"resultsonanyinterpreteroflevelKorhi~her.
Bythiswemeanthataslongastheconmandsanddatatakeadvantageonlyofstrictlydefinedoperations,similarpicturesshouldresult.
Aspectsoftheprotocolwhicharenotstrictlydefined(atthistime)includecharactersize,characterpositionrelativetothebeam,howcontrolcharactersintextoutputaffecttheterminaland'whathappenswhenthebeamismovedoralinedrawnoutsideofthelogicalscreenboundary.
Thisruleforcesupwardscompatibilltv,sothatanapplicationwrlttenusingfeaturesofalownumberedlevelwillstillworkatsiteswhichhavemovedontoimplel7lenthigherlevels.
Additionally,anyaspectsofthisprotocolvzhlchareexplicitly"leftunspecified"inthedetailedoperationsdescrlptionsbelowshallanypublicdescriptionofanactualbeexplicitlyspecifiedimplementation.
in\~enowdescribethefrarneworkwhichwillbecommontoalllevels.
BasicDataFormsInformationintheNetworkStandardGraphicsProtocolwillbeexpressedasasequenceofa-bitbytes.
Acommandwillconsistofacommandbytefollowedbyzeroorriorearaurients,Tilesanecommandbytewillalwaystakethesamenumberofargumentsinthesaneform.
Thelengthofeachargumentmaybefixedorvariable-2",;,~jdependingontheargument.
Asimpletypeofargunentisa"value,"whichisan8-bitinteger.
Anothertypeofargumentisa"string"whlchisacountfollowedby(count)numberof8-bitbytes.
Ifthecountisbetween"and127,itissentinasinglebyte.
Ifthecountisbetween128and2**15-1(**meansexponentiation),itissentintwobyteswiththehiehorderbitofthefirstbytesettoone.
Thefirstbytecontainsthesevenhighorderbitsofthenumberandthesecondbytecontainstheeightloworderbits.
Astringistheonlytypeofargunentofaco~mandwhichcanvaryinlength.
Forexample,wheneveraconmandhasoptionalarguments,theywillberepresentedinsideofastring.
CoordinatedataengenderedcosiderablediscussionatthesecondI~etworkGraphicsGroupmeeting.
Itwasdecidedthatatwo-dimensionalLo~icalCoordinateSyste~wasrequired,andeachinterpreterforthegraphicconmandbytestreamwouldberesponsibleformappingthiscoordinatesystemtophysicaldevicecordinates.
Itwasdecidedthatdatainthelogicalcoordinatesystemwouldbeintwos-complementnotation,thatitwouldbefractional,thateachedgeofthescreenwouldhaveunitlength,andthattheoriginwouldcorrespondtothecenterofthescreenontheoutputdevice.
Thevertical(horizontal)edgesofthescreenoftheoutputdevicecorrespondtothe1inesX(V)=-1/2orX=+1/2-ewhereeisasmallpositivenumberdeterminedbytheprecisionofthefractionaldata.
Particularlythepoints(-112,-112)(-1/2,l/2-e),(1/2-e,-1/2)and(1/2-e,1/2-e)shallbevisiblepointsatthecornersofthelogicalscreen.
(Inthecaseofanon-squaredisplaysurface,theimplementermaymakehisowndecision.
ThusweshallsaythattheLogicalCoordinateSystemcontainspointswhosecoordinatesrangefrom-1/2toa1ittlelessthan+1/2.
Commandswhichtakecoordinatedatawillbeavailableinvariousmodes.
Inabsolutemode,apositionisspecifiedbygivingitscoordinatesintheLogicalCoordinateSystem.
Inrelativemode,thedifferencebetweenthecoordinatesofthepositionandthecoordinatesofthecurrentpositionmustbespecified.
Thusacoordinatedatumwhichisanargumentforanabsolutemodeoperationshouldbeintherange-1/2to+1/2-e,whileoneforarelativemodeoperationshouldbeintherange-l+eto+l-e.
InterestwasexpressedatthesecondGraphicsGrouPMeetingineventuallyallowin~averylar~ecoordinatespace(manybitsofprecisionineachfractionalcoordinate).
ThisistobedonebyperrnlttIngthelength,ing-bitbytes,ofeachcoordInatedatumtobeset(asamode).
Itwasdecidedatthemeetingthattwobytespercoordinatewouldsuffice"fornow,Thus"e"intheabovediscussionis2**(-15)(oneintheleastsignificantbitofa15-bitplussignfractionalcoordinate).
-3/Textdatawillbetransnittedasanarp,umentofvariouscommandsfordisplayontheoutputdevice.
NetworkASCIIwillbeusedtorepresentcharacters.
Atthelowest-levelsoftheprotocolonlyonecharactersizewillbeavailable--whateveris"normal"onthedisplavdevice,Ifthedevicehasno"normal"size,72charactersper1inewouldbedesirable.
Athigherlevelsthesizeofeachindividualcharactercanbespecified.
Also,atthelowestlevels,controlcharacterswillbepassedalongtothedeviceforittodothebestitcan.
However,theconsensusofthegraphicsneetin~wasthatatsomereasonablylow(butnon-zero)level,carria~ereturn,1inefeed,andbackspaceshouldbeinterpretedtodotherightthing.
PictureSubroutinesandRelatedTopicsAtthesecondNetworkGraphicsGroupmeeting,itwasdecidedthattwosortsofpicturesubroutinesweredesirable,theprimarydistinctionbetweenthenbeingrelativedifficultyofimplementation.
Atthemeeting,thesimplervarietywascalledasubpicture,andthemorecomplexwascalledasubroutine.
Thisauthorbelievesthatthesetermsdonotembodyemoughsemanticstofacilitatekeepingthetwostraightandsoproposestostandardizeon"simplesubpicturelland"fullsubpicture"instead.
Theonlyparameterwhichcanbepassedtoasimplesubpictureisthe"currentbeamposition.
"Inotherwords,ifsuchasubpictureiscalledmorethanonceinapicture,theonlydifferenceinappearancebetweenthevariouscallsisatranslationduetothebeanpositionatthetimeofthecall.
Fullsubpictures,ontheotherhand,takeparameterswhichcancausesealing,rotation,reflection,oranythingelsewecomeupwith,Itisplannedthatasubpicturedefinitionneedbetransmittedonlyonce(pernetworkconnection)andwouldnotbedeletedbya"newpicture"operation.
Thusachangingpicturecouldbesubdividedintoseveralpartsonabasisofstaticversuschanginginformation;onlydefinitionsofpartswhichchangeneedbetransmittedtoredrawthepicture.
TraditionallY,picturesubroutineswhichdependonlyontheinitialbeampositionhavebeenrestrictedtorelativedatamodedrawingoperations.
Inviewofthefactthatsubpictureswillprobablybeusedtosavestaticpictureinformation,itisdesirabletoallowabsolutedatamodeoperationsinsimplesubpictures.
Thenextquestionnaturallyarises--whatdoesabsolutedatarmeaninafullsubpicturewhichtakesbothpositionandscaleparametersIsabsolutedatareallyabsoluteinthiscaseThisauthorbelicvesthattheanswerisasfollows:thefull-4,/",subpictureisreallyapictureinitsownright,soithasitsownlogicalcoordinatesystem,anditsabsolutedataisreallywithinthiscoordinatesystem.
Thus"shiftingandsealing"afullsubpicturereallymeans"scalethesubpictureinitsO\'Jncoordinatesystemandshifttheresultasawhole.
"Insummary,then,amajordifferencebetweensiMPleandfullsubpicturesisthatafullsubpicturehasitsownlogicalcoordinatesystemandasimplesubpictureusesthelogicalcoordinatesystenofwhoevercallsit.
Thisdistinctionisthereasonwhyfullsubpicturesarehardertoinplementthansimplesubpictures.
Anotherpointdiscussedatthemeetingwasaspecialdatamodewherebyasubpicturecandisplaydataatabsolutepositionsonthescreen,i.
p.
.
,absolutp.
lyinthemain(picture)program.
Toachievethis,therneetlneproposedspecialdatamodesfor'thethreeoperations:movebeaminvisibly,draw1ine,anddisplaydot.
Theintentofthesedatamodeswastobypassallfotation,sealing,andcllppingfunctionsassociatedwiththecurrentlevelofsubpicturenestinguntilthismodewasclearedinacertainway.
Thissameeffectcanbeachievedmoredirectlyandimplementedmoreefficientlybyt\JOcommandsronetosaveandonetore-establishthelogicalcoordinatesystemforthecurrentsubplcture.
(Additionaly,ofcourse,the"save"operationwouldestablishtheinitial,highestlevel,loglcalcoordinatesvstern;)SimpleSubpictureCallsBesidestheofthesubpicturetobecalled,asimplesubpicturecallmayspecifytwooptionalparameters;thefirst.
isanwhichisthe"name"(inasensedescribedbelow)ofthisparticularsubpicture~andthesecondisanabsolutepositiononthecallinr,pagetobeinvisiblymovedto,priortocallingthesubplcture,\'Jhen(eventually)thevlewerisallowedtointeractby"picking"informationdisplayedbeforehim,iftheinformationispartofasubpicture,thenthe"name"ofthesubpicture~willbepartofthe"graphicinput"reportedtotheservinghost.
Ifthelnformatlonpickedbythevieweriswithinseverallevelsofsubpicturecalls,thenar1esofeachofthecallswillbereportedinamannerwhichindicatestheirnestIng,(Notethatjustthenameofthesubplcturebyitselfisnotsufficient,sinceonesubpicturemaybedisplayedinseveralpositionsandtheapplicationmaywishtodistinguishbetweenindividualcalls.
)Iftheidentifierisnotspecifieditdefaultstothenullstring.
Iftheposition(fortheinvisiblemove)isnotspecified,thecurrentbeampositionisused.
Whichofthesetwoparametersarepresentisencodedbytwobitsinacodebytewhichpreceedstheparameters.
Ifbothparametersarepresentthentheyarealwaysinthesameorder;thisorderandthebitsofthecodebyteassi~nedtothetwoparametersare-5,IspecifiedinthedetaileddescriptionoftheSimpleInstancecommand(andintheBNFinAppendix1).
Preceedingeventhecodebyte,andimmediatelyfollowingthenameofthesubpicturewhichisbeingcalledupon,isacountofthedataintheremainderoftheinstancecommand.
Thusisincludedsothatitisnotnecessarytodecodethecodebyte"todeterminethetotallengthofanyoneSimpleInstanceoperation.
\Jindm·Jing:elippingfnotbeheldresponsiblefordoinganythingreasonableincaseapicturedisplaysinformationbeyondtheed~eofthescreen(e.
~.
,byrelativemovesanddraus).
Theinterpretermustreactproperlytothenextabsolutedataintheproperrange,however.
Varioussolutionstothissituationinexistinggraphicssystemsinclude:cllpplngalinetodisplayasmuchasisproper,blankingthewholeofalineifanypartisinvisible,ordiscardinghighorderbitsofthecurrentpositionregister,sothatnoinvisiblepositionscanberepresented(llwraparound").
Inadditiontoproble~sofedgeeffectsatthehighestlevel,problemsarisewithrespectto(full)subpictures.
Itisnicetobeabletoselectarp.
ctangularportionofasubpicturetobedisplayedaspartofasubolcturecall.
(See:~lewli1an,Displayprocedures,CommunlcatlonsoftheACt~,Volune14,Number10,October1971,pp651-660).
Inaccordancewiththeconsensusofthemeeting,whichwastomakethiscapabilityoptional,thisauthormerelyhopestoincludeintheprotocolamethodofencodingthisinformationsincehissitea)carihandlesomesuchwindowing,andb)hopestoprovideaservicefacilitytoperformthisfunction.
Appendix2describeshowtoconcatenateseverallevelsofportionsintoasinglerectangulartest,aslongasnorotationsareinvolved.
Italsooutlinestheproblemsrelatedtorotationsandportioning.
-FullSubpictureCallsWearenowinapositiontoconsiderwhatmaybespecifiedaspartofafullsubpicturecall,inadditiontothenameofthesubpicturebeingcalled,whichis,ofcourse,required.
ThedatadescribedbelowvII11allbeoptional:asinglecodebytewillpreceedallthesedata;thepresenceorabsenceofoneofthe-6Jparameterswillbeindicatedbyabitinthecodebytebeingoneorzero.
Theparameterswillalwaysappearinthesameorder,Iftheyarepresent.
ThisorderisgivenbelowinthedetaileddescriptionoftheFullInstancecommand(andintheBNFinAppendix1).
Additionally,preceedingeventhecodebyte,willbeaofthefollowingbytes,includingthecodebyte.
ThusitwillnotbenecessarytodecodethecodebytetodeterminethetotallengthofanyparticularFullInstanceoperation.
OneparameterisanwhichcanbeusedtodistinguishthisparticularcalltothissubpicturefrOMallothercallstothesubpicture.
ThisparameterwasalreadydescribedunderSimpleSubpictureCalls.
Oneparameterwhichmaybespecifiedisatranslation:thiswillbespecifiedbygivingtheabsolutecoordinatesofthecenter(onthecallingpage)oftheiMageofthesubpicture;thiswilldefaulttothebeampositioncurrentatthetimeofthecall.
ArotationMaybespecifiedbygivin~a16-bitfractionintherange0to.
1111111111111111(binary)inclusive;thisfractionwillrepresentwhatpartofafullcircle(2pi)therotationis.
Thedefaultvalueofangleofrotationt/illbezero.
(Actually,therotationrepresentationschemeworksidenticallyifonethinksofitasatwo'scomplementfractionfrom-1/2tojustlessthan+1/2.
Thatis,thesanebitconfigurationsencodethesamerotation,duetotheperiodicnatureofsineandcosine.
Forexample,binaryzeroalwaysrepresentsapi;010000.
0denotespi/2inbothschemes;10000denotes1/2inoneschemeand-1/2intheother,whichcorrespondtorotationsof+piand-plrespectively,i.
e.
identicalrotatlons.
)Alsospecifyableasapartofafullsubpicturecallisarectangularportionofthecalledpicturetobeimagedonthecallingpicture(seeprevioussectionforadiscussionofclipping).
Thisrectangleisspecifiedbyitscenterandonehalfitstota1sizeinxandv,Thatis,therectang1e\'1illconsistofallpointswhosexcoordinatediffersfromthatofthecenterbynomorethanthespecifiedx-sizeandwhoseycoordinatesatisfiesasimilarcondition.
Thedefaultforthesevalueswillplacethecenterattheoriginarid~iveboththexhalfwidthandtheyhalfwidththevalueof+1/2.
Thusthedefaultincludesthe\/holeofthelogicalcoordinatesystemofthecalledpage(andalsosomepointsoneofwhosecoordinatesare+1/2,which,strictlyspeaking,1ie"outside"ofthecoordinatesystem;howthisinconsistancyisresolvedisleftunspecified).
Finally,onemustspecifythesealiny,tobeappliedindeterminingtheimage;thiscanbedoneinmanyways.
Onewayis-7/tospecifyaunifor~~agnificationtobeappliedtothesubpicture.
Sothatmagnificationsinawiderangecanbeachieved,itistheauthor'sopinionthatsomeformofscientificnotation(i.
e.
,floatingpoint)willhavetobeemployed.
Ifthereisalreadyanetworkstandardfloatingpointnotation(whlchIamnotawareof)itshouldbeemployed.
Failingthat,Itissuggestedthatthisnotationconsistofana-bit(two'sconplement)exponentfollowedbya16-bit(two'scomplement)fractionalpart.
Anotherformofsealingistospecifyseparatema~nificationsinxandiny,tobeapplledtothesubpicturebeforeanyrotationisperformed.
Yetathirdwayistospecifyarectangularareainthecallingpicture'scoordinatesystemtobefilledwiththeimageofthesubpicture.
Sincethecenteroftheimageisalreadyspecified(bythetranslation),thisimageinformationconsistsonlyofhalf-edgesizedata.
Ifnoneofthethreemethodsofsealingarechosen(andanaffinetransformation(seebelow)isnotgivenexplicitly),thenauniformmagnificationofunity(i.
e.
,nosealing)isused.
Notethatthethreeformsofsealingtendtocontradicteachotherandonlyoneofthemshouldbeusedinanyonecall.
WhathappensIfself-contradictoryinformationisgiveninthesefieldsisleftunspecified.
Appendix.
2presentsthe~athematicsinvolvedintransformingthesubpicture'scoordinatesystemintothecallingpicture's.
.
:coordinatesystem.
Itisshowntherethatalltheindividualoperations(seallng,rotating,andtranslating)canberepresentedasasingleaffinetransformation(whichconsistsof6values).
Itmightbenicetopermittheservin~programtospecifythistransformationdirectly.
Accordingly,onepossibleparameterofafullsubpicturecallwillconsistofsixfloatingpointnumbers(oftheformdescribedundermagnification,above)tobeinterpretedasanaffinetransformatlon,i'ldeed,ifthe-affinetransformationhasthefollowingform:LIxIy_/=Lxy/*/LllLI2/+LTlT2/LL21L22_/thenthevaluesshall(arbitrarily)besentinthefollowing(columnar)order:Lll,L21,L12,L22,T1,T2.
Thisaffinetransformationshouldbeinvertible;thatis,LI1*L22-L21*L12shouldnotbezero.
Yie\'JportjngAnothertopicdiscussedatthemeeting,andreferredtotheprotocolcon~itteefordecision,wasthecapabilityofplacing.
1t11II·theopevepictureInsomerectangleofthevirtualscreen.
Thedefaultrectanglemightbethefullscreen.
Alternativelyitmightbeleftuptothevlewertospecifythedefault(Y.
.
.
L2.
)interactionwiththegraphicssystemattheUsingHost).
In-8~-'1'general,viev,portingallowsmorethanone"toplevel"picturetobeviewedatonce.
Thedesiretoviewseveraldifferentpicturesonthesamescreenarisesincasesv.
heremultipleusersareworkingtogetherandincaseswhereoneuserisinteractingwithagroupofapplications(inseparateservinghosts>.
Thisauthormaintainsthatthecoordinatetransformationsrequiredbythisfeaturearesimplerthanthatof"fullsubpictures"sincenorotationsareinvolved,andwouldbepartofthesamemechanisminitsimplementation.
Inparticular,merelyanotheraffinetransformation(seeAppendix2>wouldbeaddedtothelevelscausedbyfullsubpicturecalls.
Allthatisrequirediskeepingtrackofviewportidentifiersandtheassociatedrectangles.
Sincelittleextraworkisinvolved,itisproposedthatthisfeaturebeincludedatso~ehighleveloftheprotocol.
CommandCodesEachcommandinthegraphicsprotocolwillheassignedanon-negativevaluewhichwillrepresentthiscommandinthebytestream.
Thealgorithnwherebyvaluesandcommandsareassociatedis,itturnsout,averytouchysubject.
Therearefiveortendifferentcriteriafora"best"algorithm,eachcriteriondifferentinemphasis.
ThisGordianknotwillbecut,Inthisproposal,byorderingtheco~mandsapproximatelyaccordingtolevel,andthenjustnumberingthem.
Inaddition,ifseveralcloselyrelatedcommandsoccuratthesamelevel,someattemptwillbemadetoencodevariationsofmeaningsintermsofbitconfigurations.
Evenifsomelaterconsiderationcausesachangeinorderingtobeproposed,itisthiscommittee'sfeelingthatthenumberingshouldnotbealtered.
However,untilthismatterisfirmlysettled,itisstronglyadvisedthatanyimplementationtakeintoaccountthepossibilityofreassignmentofcommandcodes.
ParticularProposalforLeyel0ProtocolItisproposedthatlevel0bekeptverysimple.
ThisissothatimpleDentationcanbequicklyaccomplishedandexperimentationwiththeprotocolbegun.
Anotherreasonisthattheleastpowerfulhostandevenprogrammableterminalsshouldbeabletoimplementit.
InaccordancewIththis,the"rule"wasmadethatacommandbeincludedonlyifitsoutputisafunctionsolelyofthecurrentcOr.
lDandandthe"beamposition"currentatthestartofthecommand.
Inotherwords,theinterpreterforlevel0needhavenointernalstoragefor"modes"orpushdownstacks.
,.
.
,riththisrestrictionitishopedthataverysimpleimplementationwillbepossibleforlevelo.
Inparticular,perhapsonecouldeventuallybuildahardwaretranslatorfromlevel0codetoone'sownparticularterninal'scode.
Notethatintheopcodeassig~nentforlevel0,bits4,2,and1havespecialmeaningforthemove,line,anddotcommands.
In-9particular,the1bitencodesabsoluteversusrelativedatamode,the4bitencodeswhetheranyvisibleoutputoccurs,andthe2bitdetermineswhetherthevisibleoutputisalineoradot.
Level0;CommandSummaryThefollowingisa1istofcom~ands(andtheirsyntax)inlevelzero.
Detaileddescriptionsofthesecommandsfollowinthenextsection.
CommandsdealingwithprotocolmaybeaddedbytheConnectionCommittee.
(Theycurrentlyrequestopcodesintherange128to255.
)(AsdescribedinBasicDataForms,above,,,andaretwo-bytecoordinatevalues,isacountfollowedby(count)manybytesandisaneir,htbitnumber.
)DecimalOctalBinaryFormato000000000Nu111100000001Erasescreenandresetbeam2200000010MoveAbsolute3300000011MoveRelative4400000100DrawAbsolute5500000101DrawRelative6600000110DotAbsolute7700000111DotRelative81000001000Text91100001001TextR1'01200001010EndofPicture111300001011EscapeLevel0;Com~andpescriptionsoNullStatement(IINULL").
Thisstatementhasnoar~uments--andnoeffect,either.
1Erasescreenandresetbeamtoorigin("ERASE").
Thiscommandindicatesthata·newpictureisabouttobedrawn.
Itshouldalwaysbe(eventually)pairedwithafollowingEndofPicturecommand.
2Movebeaminvisiblytoabsoluteposition(It--10VEA").
IJothingisdravm;thebeamispositionedtothespecifiedabsolutex,yposition.
3Movebeaminvisiblybyrelativeamount(IlMOVER").
IJothingisdrawn;thebeamisshiftedbythespecifiedamountin-10,.
.
.
·1xandv,4Drawlinetoabsoluteposition(IlDRA~'JAIl).
Alineisdrawnfromthecurrentbeampositiontothespecifiedabsolutex,yposition.
5Draw1inctorelativeposition(IlDRA~'JR").
Alineisdrawnfromthecurrentbeampositiontothepositiondeltaxanddeltayaway.
6DisplayaDotatabsoluteposition(IlDOTAIl).
Thebeamismovedinvisiblytoabsolutepositionx,yandadotisdisplayedthere.
7DisplayaDotatrelativeposition(IIDOTR").
ThebeamismovedinvisiblYbythespecifiedamountinxandyandadotisdisplayedthere.
8Displaytext("TEXT").
Atthecurrentbeamposition,displaysomecharactersatthenormalsizeforthedevicebeingoperated.
consistsofafollov/edbycountmanycharacters.
Ifthereisno"normalsizes"choosethesizesothatseventv-itwocharactersaredisplayedperline.
ThecharactersinthestringarecodedinnetworkASCII;allcodesbetween0and127(decimal)inclusivearepermitted.
(Atlevelzero,whathappenstocontrolcharactersisleftunspecifie~.
)~herethebeamis,followingexecutionofthiscommand,isleftunspecified,exceptthatanotherDisplayTextcomnandimmediatelyfollowingwillappenditstexttothepreviousstring.
(TheuseoftheTEXTcommandisdiscouraged;useTextRinstead.
)Thepositionofthefirstcharacterrelativetotheinitialbeampositionisleftunspecfied.
9Displaytextandrestorebeam("TEXTR").
Atthecurrentbeamposition,displayastringofcharactersatthenormalsizeforthedevicebeingoperated;thenrepositionthebeamtowhereitwasbeforethecommand.
consistsofafollowedbycountmanycharact~rs.
Ifthereisno"normalslzes"choosethesizesothatseventy-rtwocharactersaredisplayedperline.
ThecharactersinthestringarecodedinnetworkASCII;allcodesbetween0and127(decimal)inclusivearepermitted.
(Atlevelzero,whathappenstocontrolcharactersisleftunspecified.
)Thepositionofthefirstcharacterrelativetotheinitialbeanpositionisleftunspecified.
-11.
.
--,10EnJ0fPicture(liENDPICII)Thiscommanddenotestheendofanewpicture.
ItmustbepairedwithapreceedingERASEcommand.
11Escapetodevicespecifics("ESCDEV").
If"value"isthecodeasslrmed(bytheProtocolCommittee)tothedevicebeingoperated,thentransmittheeight-bitbytesin(whichstartswithaindicatin~thenumberofbytes)tothedevicewithoutexaminingthem.
Otherwiseignorethiscormand,Ifthedevicedoesnotaccepta-bitinformation,reformatthedatainsomedevicespecificway;anexamplewouldbethrowingawaythehi~horderhitforasevenbitdevice,orgathering58-bitbytesintoone3G-bitword,againdiscardingthehighorderbits,perhaps.
Theactionofthebytesinthestringshouldleavealone(oratleastrestore)anyhardwarebeampositionregistersinthedevicewhichtheinterpretermightconcievablydependon.
Thiscommandreallyshouldnotbeused;itwasincludedatlevelosothatspecificapplicationscandomodesettin~andotherdevicespecificmanipulations.
Forexample,ARDSterminalsmayoptionallyhaveseveralindependentlyaddressableoutputscopes.
TheselectionmechanismchangesstateonlywhenaparticularsequenceofASCIIcharactersreachestheterminal.
ThusESCDEVwouldbeusedtoselectwhichscope(s)is/aretobeaffectedbyfollowingcommands.
(ThecurrentstateisinvisibletothegraphicspackageattheUsingHost.
)Further,supposethatanothernakeofterminalhasasimilaroption,whichrespondstoadiferentcodesequence.
ThisposslbllityisthemotivationforconditionallyignoringtheESCDEVcommandbasedonthe""specified.
GiventhataparticularapplicationwillonlybeusedtooutputtoeitheranARDSorthissecondmake(withthemultiplescopeoption),thentheapplicationcouldalwayssendtwoESCDEVcommands,oneapplicableonlytoARDSterminals,andtheotherapplicableonlytothesecondmake.
-12LEVEL1*SetLinemode(ILINf.
'IOn").
Thiscommandsetsthecurrent1inemode;possiblemodesandthe.
.
.
.
hlchsetseachare:solid(0),dashed(1),dotted(2),andothers(3or.
Atthebeginningofanewpicture(i.
e.
,afteranEraseandResetco~nand),1inemodeissolideIfasitedoesnothaveacertainmodereadilyavailable,itmaya)simulateitinsoftware,b)substituteanotherinitsplace(dashedfordotted,orviceversa)c)ignoreitentirely.
Whatisprovidedshouldbeclearlyindicatedinanypublicdocument.
Itisstronglyrecommendthatatleastsolidandoneothermodebeprovided.
*Setintensity(IISETINTII).
Thiscommandsetstheintensityof1ines,dotsandcharactersdisplayedfollowingthecommand.
Ifis128decimal,normalintensityshouldbeset.
Ifis255decimal,brightestshouldbeselected,andifitis0,thenthebeamshouldbeblanked.
Intermediatevaluesshouldbemappedappropriatelyastheimplementerseesfit.
Forinstance,ifbrightestisthesameasnormal,allvaluesfrom128through255shouldbemappedtonornal.
Informationdisplayedbetweenthestartofanewpicture(theERASEcomnand)andthefirstSETINTcommandappearsatnorrnalintensity.
*Textout("TEXTO").
Startingfromthecurrentbeamposition,thisCOmManddisplaysthe(ofnetv.
orkASCIIcharacters)formattedasifitweretypedmaterial(atthecurrentintensity).
consistsofafollowedbycountmanycharacters.
Thatis,textextendingpasttheri~htmar~in\"il1bebrokenandrepositionedattheleftmarginonthenext1inedown.
Ofthecontrolcharacters,onlycarriagereturn,1inefeed,andbackspacearerequiredtobeinterpretedproperly.
*Subpictureheader("SUBIIED").
Thiscommandbeginsthedefinitionofasubpicturenamed"lI.
ThisdefinitionisterminatedbyamatchingSUBENDcommand.
Thedefinitionwillberemembereduntilanewoneisspecifiedoruntilthegraphicsnetworkconnectionisbroken.
Notethatisaconsistingsolelyofcapitallettersandnumbers.
Subpicturedefinitionsmaybenested;thiswillbeequivalenttotransmittingthetwodefinitionsseparately.
Inotherwords,allsubplcturenamesareglobalsandare"knm'm"toallothersubpictures.
Ifasubpicturedefinitionhasnotbeenreceivedpriortoitsuseinapicture,theemptysubpictureshouldbedisplayedinitsplaceuntiladefinitionisreceived.
-13Asubpicturedefinitionneednotbetransmittedaspartofapicture(i.
e.
,withinanERASEandENDcommandpair).
Indeed,allsubpicturedefinitionsmightpreceedthemainpicture.
Currently,thewillalwaysbe1,indicatingonlyonebyteoffollows,butathigherlevelsoftheprotocolroomforexpansionmayberequired.
Inthe,the80hexbitwillbesetifthissubpicturecanbeasimplesubpicture,andthe40hexbitwillbesetifthesubpicturecanbeafullsubpicture.
(Itispossiblethatonesubpicturecanbeboth.
)Otherinformationthatmaybevenuall~bepresentinincludewhetherthecurrentvalueofacertainmodeorparametershouldbesavedonentryto,andrestoredonexitfrom,thissubroutinewheneveritiscalled.
Thesemodesandparadatametersinclude:length.
1inemode,intensity,charactersize,and*Subpictureend(IISUBENDII).
Thiscommandendsthedefinitionofasubpicture.
EachSUBENDmustmatchapreceedingSUBHEDcommand.
*Simpleinstance(1IIUSTS")Thiscommandindicatesthatthesubpictureistobecalled(instanced>'Atthislevel,level1,nosubplcturemaycallanother;ifonedoes,whathappensisleftunspecified.
Also,thismustbeacalltoasimplesubpicture.
Thusthe80hexbitofthesinglebyteofmusthavebeensetintheSUBHEDcommandwhichstartedthedefinitionof.
Ifthesubpicturehasneverbeendefined,theemptysubpictureshouldbedisplayedinitsplace.
"Thebeginswithacountoftheamountofinformationwhichfollows.
Thiscountmaybezero.
Ifnon-zero,thenextbyteisacodebytetobeinterpretedtoseewhatfurtherinformationfollows.
Ifthe30-hexbitisset,nextinthebytestreamisan(calledliASlnforrnetton").
ThisisthenameofthisparticularinstanceofthesubpictureasdescribedunderSimpleSubpictureCalls.
Ifthe40-hexbitisset,thennextinthebytestream(followingtheASinformation,ifpresent)isanx,yposition(inthecallingpicture'scoordinatescheme)atwhichthesubpicturewillbecentered.
(ThisiscalledATinforMation.
)IfATinformationisnotspecified,thecurrentbeampositionisusedasadefault.
IfASinformationisnotspecified,itdefaultstothecontainingzerocharacters.
Ifneitherthe40hexnorthe80hexbitsareset,thenneithertheATinformationnortheASinformationispresent,andthecodebyteshouldbezero.
(Also,thelengthcounthadbetterbe1.
)-14/Changestolevelacommandsforlevel1.
TEXTandTEXTR--Carria~ereturn,1inefeedandbackspacecharactersshoulddefinitelYbeinterpretedwhenevertheyappearIn.
Theresultsofothercontrolcharactersremainunspecified.
TheintensityofthecharactersshallbeaffectedbytheSETItJTcommand.
ERASE--Normalintensityandsolid1inemodemustbeestablishedatthestartofanewpicture.
DRAWAandDRAWR--LinemodeandintensityshallbeaffectedbytheLINMODandSETINTcommands.
DaTAandDOTR--IntensityshallbeaffectedbytheSElINTcommand.
-15LEVEL2*1·lark("I·:ARI~").
Thiscomnandcausesthecurrentx,ybeanpositiontobesavedonapushdownstacl:.
Thispushdownstackr.
1UStbeseparatefromthesubplcturecallpushdownstack.
*l·iovetonarkandpop("I·OV:::r:I~II).
Thiscommandsetsthecurrentbearipositionequaltothex,ypositionatthetopofthe"riarl.
"oushdov.
nstack.
Ifthestackisempty,theorlrtinisuseJ,instead.
Thenthestackispoppedup(un1essitisernpty).
*Drav/tomarkandpop("Dr:,\\:'I:I'.
").
Ifthe"rnark"pushdov.
nstacl:isnotermtv,thlscormanJ~Ira\"lsa1ine(ofthecurrent1inel'~odeandIntensitv)fromthecurrentbeanpositiontothe;ofthe"mark"pushdownstacl:,andsetsthebeartr>OSitiontothatvalUP.
.
Thenthestackispopped.
Ifthestackiscriptv,the1inei~:drav.
ntotheori~inandthebeanpositionissett~erealso.
ChanxestolevelUand1farlevel2.
Ir!
STS--arbitrarylevelsofsIrnplesubnlcturesnusthesupported,(IlotethatrecursiveuseofsubpicturesisnotalLowed:oncerecursionstarts,itcanneverbestopped;)Thepushdownstackforsubplcturecallsrnustbekeptseparatefror.
lthe"mark"pushdov.
nstack.
-lG,ILeve13(Perhapsallrotationaltransformationsshouldbeputatahlzherlevel,forinstancehigherthanviewportoperations.
)*FullInstance("ItJSTF")Thiscomnandindicatesthatthesubpictureistobecalled(instanced)ina"fullIImannerasdescribedinanexplanatroysection.
Foronething,thismeansthatthe40hexbitofthesinglebyteofmusthavebeensetintheSUBHEDcommandwhichstartedthedefinitionof.
Ifhasneverbeendefined,theemptysubpicture(i.
e.
,nothing)shouldbedisplayedinitsplace.
TheissimilartothedescribedundertheIr~STScommand,buttheformercontainsmoreinformation.
Belowisa1istoftheinformationwhichcanbespecified,andthebitassignedtothepresence/absenceofeachpieceofinformation.
Thepiecesofinformationwhicharepresentalwaysappearinthebytestreamintheordertheyaredescribedinthis1ist.
(AllthepiecesofinformationaredescribedmorefullyinFullSubpictureCalls,exceptfortheliAslnforruatlon"whlchisdescribedinSimpleSubpictureCalls,)Bit(hex)Information80Asinforrlation--IInamellofthisparticularinstance.
Consistsofan.
40Translationinfor~ation--Centerofthesubpicture'simageonthecallingpage.
Consistsofananda.
20Rotation--Fractionalpartof2pitorotatetheimagecounterclockwise.
Consistsofa16-bitunsignedfraction.
10PortionInfornation--Rectangularpartofsubpicturevrhlchistobedisplayed.
Consistsof,,.
8Uniform~agnification--Amounttoscalethewholesubpicture.
Consistsofafloatingpointnumber(whichshouldnotbezero).
4Separatexandymar,nification--Separatescalesforthexandyaxesofthesubpicture.
Consistsoftwofloatingpointnumbers(neitherofwhichshou1dbezero)2ImageSize--Howlargearectangleonthecallingpageistheima~etooccupy.
Consistsofanandapartofthewouldincludethissecondcodebyteandanyadditionalbytesofinformation.
*Escapetotoplevelcoordinatesystem("ESCTOp").
UntilaRESLEVco~andis(subsequently)executed,alldisplaycommands(moves,draws,dots,andtexts)shalloperateasiftheywereissuedbythetoplevel(main)pictureinsteadofthesubpicturecontainingthem.
Thatis,theyshallbemappedtothescreenaccordingtothemapforthehighestlevel.
Subpicturecallsthemselves,whicharemadewhileanESCrapcommandisineffect,arenotaffectedbythecommand.
Thatis,transformationsarecalculatedasifthecommandwerenotineffect.
Thecalculatedtransformationsareignored,however,andinformationdisplayedbythesubpicturestillappearstobeatthetoplevel,untilaRESLEVcommandnullifiesthe[SCTapmode.
ThusasubplcturecallexecutedwhlleanESCTapcommandisineffect,,actsasifaRESLEVwereexecutedinmediatelybeforethecall,andanESCTapcommandwereexecutedasthefirstcommandofthesubpicture.
Similarconsiderationsholdforreturningfromsubpictures.
*Resurnecurrentlevelcoordinatesystem("RESLEV").
Thiscommandrestoresthelogicalcoordinatesystemcorrespondingtothesubpicturecurrentlyexecuting,incasethatcoordinatesystemwasdisabledbyan[SCTapcommand.
(SeeESCTap.
)Changestolevels0,1,and2forlevel3.
MARK--thesavedbeampositionshallbeintermsofthelogicalcoordinatesystem,notthephysicalcoordinatesystem.
TEXTR,TEXT,TEXTO--Sinceafullsubpictureissupposedtobetransformaedasawhole,asifitwereapictureinitsownright,itappearstothisauthorthat,inparticular,allbeammovementsrelatedtocharactersshouldbeaffected.
Thisincludescharactersize,tab,carriagereturnand1inefeed.
Inparticular,carriagereturnshouldsetthebeamtotheleftmargin--thatis,totheleftedgeofthelogIcalcoordinate-18~1.
systemofthecalledsubpicture.
Allthesechan~esmaybeveryhardtoaccoMplish,andwhatshouldbedonewillbeleftunspecifiedatthistime,withcommentfromreadersparticularlyinvited.
-19Leve1.
4(Perhapsvlewportoperationscanheincludedin.
level3.
)*DeclareViewport("SETV\~lI)Settheviewportidentifiedbytorepresenttheindicatedareaofthelogicalscreen.
Thexandydataarenotphysicalscreencoordinates,sincethatwouldinvolvedevicedependencies.
Thiscommandcompletelysuperceedsanypreviousdeclarationofthesameviewport.
Ifinformationisalreadydisplayedwithintheviewportspecified,thiscommandcausesthedisplayedinformationtoberelocatedonthescreentoitsnewposition.
IftheareaspecifiedexceedstheIimitsofthegraphicsstandarddisplayscreen,whathappensisleftunspecified.
Viewportsneednothedisjoint;iriotherwords,twoviewportscanpresentdisplayinformationatthesamepointonthescreen.
Iforarenegative,theviewportnamedshouldbedeleted.
Allinformationdisplayedbyitshallnolongerappear.
Becauseitaffectsthetoplevelpicture,thisauthorfeelsthatJthiscommandshouldnotoccuraspartofapictureorinasubpicturedeclaration.
*AJdsubplcturetovlewport("ADDSV\-1")Thesubpicturenamedisdisplayedwithintheviewportspecified,ifitisnotalreadydisplayedthere.
(If.
itis,nothingisdone.
)Thesubpicture"mustbecapableofbeing~alledviaafullsubpicturecall.
Iftheviewporthasneverbeendeclared.
Y-LaaSETV\icommandv/hathappensisleftunspecified.
(Threepossibilitiesare:nothlngisdisplayed;theviewportdefaultstothewholelogicalscreen;thehumanvlewerispermittedbytheUsingHosttospecifythevlewoort.
)Iftheviewportissubsequentlydeclared,thesubpictureshallbedisplayedinit.
Ifthesubpicturehasneverbedeclared,nothingisdisplayedforit;-whenandifitissubsequentlydeclared,thenewdefinitionisdisplayedintheviewport,norethanonesubpicturemaybedisplayedinasingleviewportatonce.
Becauseitaffectsthetoplevelpicture,thisauthorfeelsthatthiscommandshouldnotoccuraspartofapictureorinasubpicturedeclaration.
*Clearviewport(IlCLV\"I")AllsubpictureswhichhavebeenaddedwiththeADOSVWcomMandto-20Itheviewportspecifiedinthisco~mandareremovedfromit.
Thusthespecifiedviev/portcontributesnothingtowhatthehumanviewersees.
(AfteraCLVW,theareaoftheviewportmaynotbeblankduetoother,non-clearedviewportswhichoverlapit.
)Becauseitaffectsthetoplevelpicture,thisauthorfeelsthatthiscommandshouldnotoccuraspartofapictureorinasubpicturedeclaration.
Changestolevels0,1,2,and3forlevel4.
ERASE--Allviewportsarecleared(asintheCLVWcommand)buttheirdeclarationsarerernernbered,ENDPIC--Thiscommandpartiallylosesitspurpose:itnolongerservestomarktheendofallpictureinformationtobepresentedtotheuser,sincevicv/portoperationsmayfollowwhichamendoralterthepicture.
ThisfunctionispartiallytakenoverbytheDELAYandNODELAYconnandsdescribedbelow.
-21II(-.
\.
Leye1*SetCharacterSizf!
(IISETCHSII).
Untilfurthernotice,charactersshallbedisplayedsothateachoccupiesapproximatelyandintheappropriatecoordinatedirectioninthecurrentlogicalcoordinatesystem.
Inter-characterandinter-linespacingcouldbecertainpercentages(anyideas)morethanand,ortheycouldbespecifif!
dseparately.
Inanycase,onlyaIIbesteffort"wouldbeexpectedatasite.
Charactersizeisalwayssettonormal(asdefinedbylevel0charactersizebeingnormal)bytheERASEcommand,andshouldbepositive,exceptthatifisequaltozero,thenbeingnegative,zero,orpositive,correspondtoacharactersizewhlchis"sraallerthannormal","normal,"or"largerthannorrnal;.
"Howmuchsrnallerorlargerthannormalisleftuptothesite.
Changestolevels0and1forlevelTEXTR,TEXT,andTEXTO--Charactersaretobedisplayedaccordingtothecurrentcharactersize.
ERASE--Mustestablishnormalcharactersize,normalbeingthatforlevelO.
-229Leve1I*SetDataLength("SETDLN").
UntilthismodeisexplicitlychangedwithanotherSETDLN,variousdatawillconsistofnumberofbytes.
maybe1,2,3,or4.
Affectedarethefollowingsyntactictypes(refertoAppendix1):,,,,,,,andthefractionalpartofafloatingpointnumber.
Whenanetworkconnectionisinitiallyestablished,thedatalengthistwo.
Leve1II(Thesecom~andsshouldprobablybeatthesamelevelasviewportoperations,ifnotear1ier)*ExtensiveChangesFollow("DELAY").
ThisoptionalcommandisdesignedtoeliminatefutileeffortonthepartoftheUsinr,Hostpror,rams.
Atsomehostsand/orwithsomeoutputdevices(particularlystoragetubes)anon-neg]igibleamountoftimemayberequiredtopresentanima~etothehuman.
viewer.
Ifextensivechangesaregoingtobemade,thiscOr.
lmandwouldbeusedtopreventtheUslnzHostgraphicspackagefromupdatingtheimageaftereverychan~e.
ANODELAYcommandexitsfromtheDELAYmodeandcausestheiMar,etobepreparedandpresentedtotheviewer.
Forexample,thecurrentpicturemaydisplayfoursubpictureseachofwhichis~oinr,toberedefined.
WithoutaDELAYcommand,theviewerwouldseesuccessivestagesofthechange,eachpossihlyinvolvingalargeamountofcomputationortransmissiontime.
*EndofExtensiveChanges("NODELAY")Thisoptionalco~mandundoestheeffectoftheDELAYcommand.
-23I'-\.
.
.
.
Appendix1:BNFfortheGraphicsProtocolByteStreamKeytobelow:Non-terminalsarerepresentedin.
Terminalswhicharekeywordsstandingforparticulareight-bitvaluesareincapitals.
Terminalswhosemeaningshouldbecleartothereaderareinlowercase.
Notethat"empty_string"means"zerobytes,"not"a\'Jh0seiszer0II::=empty_stringI(picture>III::=::=::=II::=II::=empty_stringI::=I::=IIIIIIIIII::=IIIIIII-24::=ERASE::=ENDPIC::=SUBHED::=aO-hexI40-hexICO-hex::=SUBEND::=SETVW::=ADDSVWlld::=CLVW::=DELAY::=r~ODELAY::=ESCDEV::=ESCTOP::=RESLEV::=IlULL::=MARK::=L1t~I~OD::=SETIIJT::=SETCHS::=SETDLN::=MOVEA::=MOVER::=DRAWA::=DRA\1R::=DOTA::=DOTR::=NOVEMKCdrawtornarkandpopstt>::=DRA\'IHK::=TEXTR::=TEXT::=TEXTO::=II:STS::=It!
STF::=eig!
"lt_bits_of_binary_OI::=bi.
tpatternindicating:whatclausesfollow::=eip,ht_bits_of=binary_OI::=er.
1pty_stringI::=empty_stringI.
~::=empty_stringI-25-.
.
.
::=empty_stringI::=empty_stringI::=empty_stringI::=empty_strin~I::=empty_stringIsix_'s::=16-bit_non-negative_fractional_part_of_a_circle::=::=::=::=::=signed,_two's-complement,_fraction_in_range-1/2tolessthan+1/2::=si~ned,_two's=complement,_fraction,range_strictlY_between_-l_and_+l::=network_standard_floating_pointnumber_if_anyI8-bit_two's_complement_exponent_partanda16-bit_two's_complement_fraction_part::=7-bit_non-negative_integerI15-bit_non-negative_integer_represented_in"excess_2**15"_notation::=count_8-bit_bytes::=count_upper_case_letters_or_numbers::=::=8-bit_integer::=8-bit_integer-26Appendix2.
MathematicalEor~ulaeforSubpicturesTransforr:1ationsInthisappendixpositionsinalogicalcoordinatesystemwillberepresentedbyarowvectorwithtwoelements,asinLxy_I.
Vectorsandmatriceswillbedelimitedbythesefunnybrackets:L_I.
varioussymbolswillbeusedtorepresentparametersinafullsubpicturecallrelatingtoatransfor~ationfromonecoordinatesystemtoanother;thesearedefinedbelow:MxandMy:magnificationsinxandytobeappliedbeforeanyrotation.
Theymaybenegativeindicatingreflection.
8anangleofrotationintherange0tojustlessthan2pi.
LIcxIcy_I:thecenter(inthecallingpicture)oftheimageofthesuhpicture.
IsxandIsy:thehalf-sizes,inthexandydirections,oftheimageonthecallingpageintermsofthecallingpage'scoordinatesystem.
Theymaybenegativetoindicatereflection.
Lxy_1:apositiononthecalledpage.
LIxly_/:thepositiononthecallingpagecorrespondingtoLxy_l.
LPcxPcy_l:Thecenteroftheportionofthecalledsubpicture'scoordinatesystemwhichistohemappedtothecallin~par,e.
ThisdefaultstoL00_1ifnotspecified.
PsxandPsy:Thehalf-sizesinxandyoftheportionofthesubpicturetobemapped.
Thesebothdefaultto+1/2innotspecified.
(.
iauniformmagnificationisspecified,s~tMxandMyequaltoitandproceedbelowasiftheywerespecified.
)Ifmaenificationsarespecified,thefollowingholds:LIxly_1=(Lxy_1-LPcxPcy_/)*IMx/PsxaI*L0My/Psy_1Icos8I1/2oI+LIexL-sinSL0112_1or,inotherwords,1)Llxly_1=Lx-Pcxy-Pcy_1*It~xcos8/2Psxt1xsin8/2PsxIL-Mysin8/2PsyMycos8/2Psy_1+LIcxIcy_I-27(Thefactorof1/2isnecessarybecause,forinstance,(x-Pcx)/Psxrangesfrom-1to+1forxvalueswithintheportion(1.
e.
,suchthatIx-PcxIspecifiedinsteadofthemagnification,wehavethefollowing:LIxly_1=(LxY_I-LPcxPcyI)*/I/Psx0/*L011Psy_IIcos8sin8'1*1Isx0I+LIcxL-sinScose_ILoIsy_1or,inotherwords,2)Llxly_1=Lx-Pcxy-Pcy_1*IlsxcosS/PsxIsysin8/PsxIL-Isxsin~/PsyIsycosS/Psy_1Expandingtheparenthesizedquantitiesinequations1)and2),wehave:3a)Llxly_1=Lxy_1*/Mxcos8/2PsxI'lxsinS/2PsxIL-~iysinS/2Psyr.
1ycosS/2Psy_1+Llcx-PcxNxcos8/2Psx+PcyMysinS/2PsyIcy-PcxMxsin8/2Psx-PcyMycosS/2Psy_Iand3b)Llxly_1=Lxy_/*Ilsxcos8/PsxIsysin8/PsxIL-Isxsin8/PsyIsycos8/Psy_1+Llcx-Pcxlsxcos8/Psx+Pcylsxsin8/PsyIcy-Pcxlsysin8/Psx-Pcylsycos8/Psy_1Variousinterestingsubstitutionscanbemadein3a)and3b).
Forexample,if8=0(norotation),thenwehave:4a)LIxIy_/=Lxv.
J/t.
1x/2Psx0I+Llcx-PcxMx/2Psx*ICy-Pcyf.
iy/2Psy_/L0My/2Psy_14b)LlxIy_/=Lxy_11IsxlPsx0I+Llcx-Pcxlsx/Psx*Icy-PcyIsvtsy_/L0IsylPsY_I-28.
.
.
.
.
.
1·Anotherexampleisifnoportioningisdone(Pex~Pey=O,.
.
Psx=Psy=1/2):Sa)LlxIy_/=Lxy_/*/MxeosSMxsinS/+LlexL-t-1yslnsMysln9_1Sb)LlxIy-'=Lxy_1*121sxcosS21sysinSI+LlcxIcy_IL-2lsxsinS21syeosS_1If,inaddition,6=0,wehave:6a)LIxIv.
:'=Lx~'ix+IexyMy+Icy_I6b)LlxIY_I=Lx*2Isx+lcxy*2Isy+lcy_/Ofcourse,inallcases,thetransformatlonfromLxy_/toLlxly_1canbewrittenintheform:Llxly_1=Lxy_1*I2by2I+Ltranslation_ILmatrix_IIngeneral,atransformationcombinin~alineartransformationandatranslationiscalledanaffinetransformation.
Transformations\\IithI!
estedLevelsThecombinationoftwoaffinetransforMationsisagainanaffinetransformation.
Indeed,ifLlxIy-'=Lxy_I*IMatI/+LTranI_IL_IandLlx'ly'_1=Llxly_1*IMat2I+LTran2_IL_IthenLlx'Iy'_1=Lxy_1*(IMatII*IMat2I)L_IL_I+(LTran2_I+LTranII*/Mat2/)L_IThusifonehasnestedfullsubpicturecalls,thedataatanylevelneedbetransfornedonlyonce,namely,bythetransformationwhicllistheconbinationofthesinglesteptransformationsateachlevelofnesting.
Anew"grandcombinationl'affinetransformationshouldbecomputedwheneverafullsubpictureiscalled(afterpushingdownthecurrenttransformation)bycombiningthecurrent~randcombinationwith-29-.
theaffinetransformationforthisparticularsubpicturecall.
PortionswithNestedLevelsAslongasnorotationsareinvolved,orevenonlyrotationsinmultiplesofpi/2,thenmultiplelevelsofportionsareeasytoimplement.
Inthediscussioninthenexttwoparagraphsletusassumethatnorotationsotherthanwholemultiplesofpi/2areinvolved.
Justasonecankeeptrackof"a"grandcombination"affinetransformation,socanonekeepap,randcombinationofportions.
Ateachlevel,onecanproceedasfollows:Saveacopyofthecurrentgrandportion,andusetheinverseofthesinglelevelaffinetransformation(specifiedinthesubpicturecall)todeterminewhatrectangleofthecalledpagecorrespondstothecurrentgrandportion(onthecallingpage).
Variousrelationsmayexistbetweenthisrectangleandtherectanglespecified(ordefaulted)inthesubpicturecall.
Theymaybedisjoint(inwhichcasethissubpictureneednotbecalledatall);theymaybeequal(aneasycase);onemaycontaintheotherorthwymaypartiallyoverlap.
Ifthere~anyintersection,itwillbearectangle,andthisrectanglebecomesthenewgrandcombinationportion.
Theproblemwithrotationsotherthanmultiplesofpi/2isthattheinverseimageoftherectangleisnolongerinthestandardorientation(verticalandhorizontaledp,es).
ThismeansthatitsIntersectionwiththeportionspecifiedonthesubpicturecallmayhave3,4,5,6,7,or8edges(ifitisnon-empty).
Deeperlevelsmaygetevenworseiftheyinvolverotationstoo.
Whiletheremaybenoconceptualdifficulty(forsome)inworkingwithsuchasituation,si~nificantlymorecomputationisinvolvedthanInthesimplehorizontalandverticaledgecase.
Thisprotocolputsforwardnorecommendationinthecasethatrotationsotherthanwholemultiplesofpi/2areinvolvedwithportions.
Itdoessuggestthatnestedportionsbehandledasdescribedaboveinthemorestr~ightforwardcase.
-30